prove that f is injective: help please!!

Consider the function f:P(N) --> R given by f(A) = . d1d2d3 . . . where the decimal expansion of f(A) is determined by the rule that di = 0 if i is not in A and di = 1 if i is in A. Prove that f is injective.

Consider the function f:P(N) --> R given by f(A) = . d1d2d3 . . . where the decimal expansion of f(A) is determined by the rule that di = 0 if i is not in A and di = 1 if i is in A. Prove that f is injective.

I am stuck on this i would appreciate any help. Thank you.

Not the neatest and clearest way to ask this question: what is i, for one? Of course, i is a natural number (i.e., element in N) and etc.

Anyway, supose A =/= B ==> there's an element in A that doesn't belong to B or the other way around, so wrg let us assume there's an element x in A that doesn't belong to B ==> f(A) in the x-th decimal digit will have a 1, whereas f(B) in the x-th decimal digit will have a zero ==> f(A) =/= f(B) and we're done.